Can't say that I have ever heard that one before, and I have heard many.

We sometimes say 'A guest home is like the God home" but on the other hand we say 'Good guests come rarely' and 'The best visit is the short one'. 
Sometimes you can get tired of someone coming to you over and over again. My mother-in-law had a friend. He was a neighbour who was lonely, so he was happy whenever he could visit her. But he started to come every evening. The discussion topics have finished quickly and after a few months he was coming just to drink a cup of tea and watch TV with her. He never proposed that they could go out or do something else together. When he was asked if he could come less frequently he felt offended and now he even doesn't answer to 'Good morning '.

It is usually acceptable if it is a robin in your garden.

It sounds better to say: "A regular guest is not welcomed."

"Constant" has to do something with quantity. For eg: My weight is constant for years.